Factorization strategies for third-order tensors

[1]  Mansoor Rezghi,et al.  Diagonalization of Tensors with Circulant Structure , 2011 .

[2]  C. Martin,et al.  The rank of a 2 × 2 × 2 tensor , 2011 .

[3]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[4]  Karen S. Braman Third-Order Tensors as Linear Operators on a Space of Matrices , 2010 .

[5]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[6]  Pierre Comon,et al.  Subtracting a best rank-1 approximation may increase tensor rank , 2009, 2009 17th European Signal Processing Conference.

[7]  Eugene E. Tyrtyshnikov,et al.  Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time , 2008, SIAM J. Matrix Anal. Appl..

[8]  Michael P. Friedlander,et al.  Computing non-negative tensor factorizations , 2008, Optim. Methods Softw..

[9]  Vin de Silva,et al.  Tensor rank and the ill-posedness of the best low-rank approximation problem , 2006, math/0607647.

[10]  M. Kilmer,et al.  A Third-order Generalization of the Matrix Svd as a Product of Third-order Tensors , 2008 .

[11]  Berkant Savas,et al.  Handwritten digit classification using higher order singular value decomposition , 2007, Pattern Recognit..

[12]  Tamara G. Kolda,et al.  Categories and Subject Descriptors: G.4 [Mathematics of Computing]: Mathematical Software— , 2022 .

[13]  T. Kolda Multilinear operators for higher-order decompositions , 2006 .

[14]  P. Hansen,et al.  Exploiting Residual Information in the Parameter Choice for Discrete Ill-Posed Problems , 2006 .

[15]  Misha Elena Kilmer,et al.  Kronecker product approximation for preconditioning in three-dimensional imaging applications , 2006, IEEE Transactions on Image Processing.

[16]  M. Friedlander,et al.  Computing non-negative tensor factorizations , 2008, Optim. Methods Softw..

[17]  Tamara G. Kolda,et al.  Higher-order Web link analysis using multilinear algebra , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

[18]  David E. Booth,et al.  Multi-Way Analysis: Applications in the Chemical Sciences , 2005, Technometrics.

[19]  Bülent Yener,et al.  Modeling and Multiway Analysis of Chatroom Tensors , 2005, ISI.

[20]  C. F. Beckmann,et al.  Tensorial extensions of independent component analysis for multisubject FMRI analysis , 2005, NeuroImage.

[21]  Fumikazu Miwakeichi,et al.  Decomposing EEG data into space–time–frequency components using Parallel Factor Analysis , 2004, NeuroImage.

[22]  Fumikazu Miwakeichi,et al.  Concurrent EEG/fMRI analysis by multiway Partial Least Squares , 2004, NeuroImage.

[23]  James G. Nagy,et al.  Iterative Methods for Image Deblurring: A Matlab Object-Oriented Approach , 2004, Numerical Algorithms.

[24]  Demetri Terzopoulos,et al.  Multilinear subspace analysis of image ensembles , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[25]  Demetri Terzopoulos,et al.  Multilinear image analysis for facial recognition , 2002, Object recognition supported by user interaction for service robots.

[26]  Demetri Terzopoulos,et al.  Multilinear Analysis of Image Ensembles: TensorFaces , 2002, ECCV.

[27]  Phillip A. Regalia,et al.  On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors , 2001, SIAM J. Matrix Anal. Appl..

[28]  M. Davies,et al.  Mathematics in signal processing V , 2002 .

[29]  Gene H. Golub,et al.  Rank-One Approximation to High Order Tensors , 2001, SIAM J. Matrix Anal. Appl..

[30]  Nikos D. Sidiropoulos,et al.  Parallel factor analysis in sensor array processing , 2000, IEEE Trans. Signal Process..

[31]  H. Kiers Towards a standardized notation and terminology in multiway analysis , 2000 .

[32]  P. Paatero Construction and analysis of degenerate PARAFAC models , 2000 .

[33]  Joos Vandewalle,et al.  On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors , 2000, SIAM J. Matrix Anal. Appl..

[34]  Joos Vandewalle,et al.  A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..

[35]  Misha Elena Kilmer,et al.  Cauchy-like Preconditioners for Two-Dimensional Ill-Posed Problems , 1999, SIAM J. Matrix Anal. Appl..

[36]  R. Bro,et al.  A fast non‐negativity‐constrained least squares algorithm , 1997 .

[37]  Raymond H. Chan,et al.  Conjugate Gradient Methods for Toeplitz Systems , 1996, SIAM Rev..

[38]  L. Lathauwer,et al.  From Matrix to Tensor : Multilinear Algebra and Signal Processing , 1996 .

[39]  J. Berge,et al.  Kruskal's polynomial for 2×2×2 arrays and a generalization to 2×n×n arrays , 1991 .

[40]  J. Kruskal Rank, decomposition, and uniqueness for 3-way and n -way arrays , 1989 .

[41]  J. Denis,et al.  Orthogonal tensor decomposition of 3-way tables , 1989 .

[42]  A. Agresti,et al.  Multiway Data Analysis , 1989 .

[43]  Pieter M. Kroonenberg,et al.  Three-mode principal component analysis : theory and applications , 1983 .

[44]  Michael A. Saunders,et al.  LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares , 1982, TOMS.

[45]  J. JáJá Optimal Evaluation of Pairs of Bilinear Forms , 1979, SIAM J. Comput..

[46]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

[47]  Richard A. Harshman,et al.  Foundations of the PARAFAC procedure: Models and conditions for an "explanatory" multi-model factor analysis , 1970 .

[48]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.